Nonlinear Adsorption Behavior Research Articles

Analysis of Factors for Compacted Clay Liner Performance Considering Isothermal Adsorption

The concentration profiles and breakthrough curves of the 2 m thick compacted clay liner (CCL) given in the specification were compared, considering three different adsorption isotherms (upper convex, linear, and lower concave). In addition, the effects of transport parameters, sorption isotherms, and source concentrations on pollutant migration were analyzed. The results showed that the dimensionless breakthrough curves of different source concentrations considering the linear adsorption isotherm coincided with each other, as the partition coefficient of the linear adsorption isotherm was constant. For the lower concave isotherm, the migration of a large source concentration was slowest, because the partition coefficient of the lower concave isotherm increased with an increase in concentration. For the upper convex isotherm, the migration of a large source concentration was fastest, because the partition coefficient decreased with an increase in concentration. The effects of the nonlinear isotherms on the shape of the outflow curve were similar to the effects of a change in the hydrodynamic dispersion (Dh): the concentration front of the upper convex isotherm was narrower, which was similar to the effect of a reduction in Dh (i.e., PL), and the concentration front of the lower concave isotherm was wider and similar to the effect of an increase Dh (i.e., PL). Therefore, the diffusion and adsorption parameters were fitted separately in the study, in case the nonlinear adsorption behavior was mistakenly defined as linear adsorption.

Aromatics/Alkanes separation: Simulated moving bed process model development by a concurrent approach and its validation in a mini-plant

SMB process development for multicomponent systems is often challenged by the difficulty of optimizing and validating a complex adsorptive separation process whose performance is strongly dependent on multicomponent nonlinear adsorption behavior. We recently proposed a “concurrent” iterative approach to simultaneously optimize SMB process design while determining the adsorption characteristics, wherein a multi-component Langmuir isotherm approximates more complex adsorption behavior in a certain range of liquid phase compositions that are relevant to the SMB design. In this report, the concurrent approach was applied to the separation of a model aromatics/alkanes mixture that approximates hydrocarbon streams often encountered in petroleum refining. In particular, we consider a nonlinear multicomponent system of toluene, dodecane and cyclohexane which have strong competition for adsorption in a mesoporous silica adsorbent. Using an approach that combines adsorption measurements, model fitting, and SMB model predictions that allow targeted selection of compositions for adsorption measurements, we demonstrate convergence of the concurrent method in three iterations with only a small number (32 in total) of multicomponent adsorption measurements. Then, we demonstrate a second iterative methodology to refine the SMB model by estimating the non-thermodynamic (i.e., mass transfer) and other (dead volume) system parameters, using only a very small number of runs on a 16-column SMB “mini-plant” designed and constructed in-house at the Georgia Institute of Technology. The final process design, validated in the SMB mini-plant, maximizes the throughput while maintaining the desired aromatic purity and recovery within an error of 1.5%. The present work thus demonstrates the idea that the SMB process can be developed and experimentally validated in an accelerated manner without requiring prior knowledge of the “global” multicomponent adsorption characteristics.

Modifier adsorption in supercritical fluid chromatography onto silica surface

The adsorption of methanol, ethanol and isopropyl alcohol on a silicagel adsorbent from supercritical carbon dioxide was investigated using nonlinear chromatographic techniques. Series of adsorption isotherm data points of these alcohols were determined by frontal analysis. Their nonlinear adsorption behavior were modeled using a modified BET equation extended for heterogeneous adsorption surfaces. Our results suggest the formation of an adsorbed multilayer of alcohols above the silica surface. This organic solvent enriched layer governs the separation of the analytes in supercritical fluid chromatographic separations, both under analytical and preparative conditions.

An analytical solution to contaminant diffusion in semi-infinite clayey soils with piecewise linear adsorption

The adsorption of contaminants onto soil particles typically is nonlinear if the contaminant concentration is sufficiently high. A simplified piecewise linear adsorption isotherm consistent with experimental results is proposed as an approximation for nonlinear adsorption behavior. This approximation allows for the use of analytical solution to model solute diffusion of contaminants that exhibit nonlinear adsorption. A moving boundary is introduced to represent significant changes in the retardation factor of clay with an increase in solute concentration. The proposed analytical solutions were validated using experimental data presented in the literature. There is negligible difference between the results obtained by the proposed analytical solution and those obtained by the linear model when C m / C 0 reached 0.5. The results also show that the model based on linear adsorption using the initial secant of the Freundlich isotherm leads to significantly lower estimated breakthrough time for the contaminant of interest than that obtained using the proposed model. The earlier breakthrough is due to an under-estimation of the amount of adsorption. The proposed method is relatively simple to apply and can be used for evaluating experimental results and verifying more complex numerical models.

Influence of adsorption on phenol transport through soil–bentonite vertical barriers amended with activated carbon

The potential for enhanced containment of phenol by soil–bentonite (SB) vertical barriers amended with activated carbon (AC) was investigated. Results of batch equilibrium adsorption tests on model SB backfills amended with 0–10 wt.% granular AC (GAC) or powdered AC (PAC) illustrate that the backfills exhibited nonlinear adsorption behavior that was described well by both the Freundlich and Tóth adsorption models. The AC amended backfills exhibited enhanced phenol adsorption relative to unamended backfill due to hydrophobic partitioning to the AC. Adsorption capacity increased with increasing AC content but was insensitive to AC type (GAC versus PAC). Results of numerical transport simulations based on the measured adsorption behavior show that the Tóth model yielded similar or lower phenol breakthrough times than the Freundlich model for the range of source concentrations ( C o ) considered in the simulations (0.1–10 mg/L). Breakthrough time decreased with increasing C o but increased with increasing AC content. Predicted breakthrough times for an SB vertical barrier amended with 2–10 wt.% AC increased by several orders of magnitude relative to the theoretical case of a nonreactive (non-adsorbing) barrier. The findings suggest that AC may be a highly effective adsorption amendment for sustaining the containment performance of SB vertical barriers.

Modeling of adsorption in hydrophobic interaction chromatography systems using a preferential interaction quadratic isotherm

A preferential interaction quadratic isotherm model for hydrophobic interaction chromatographic systems is presented in this paper. In this isotherm, the nonlinear effect of salt on the capacity factor is described using the preferential interaction model developed by Perkins et al. [J. Chromatogr. A, 766 (1997) 1]. This is then coupled with a quadratic nonlinear isotherm to describe nonlinear adsorption behavior at high solute concentrations. The resulting preferential interaction quadratic isotherm is examined for its ability to describe solute adsorption behavior under both linear and nonlinear conditions over a wide range of salt concentrations in HIC systems. The results indicate that this isotherm is well suited for predicting nonlinear adsorption behavior in HIC systems for both proteins and low-molecular mass HIC displacers.

Low-Molecular-Weight Displacers for High-Resolution Protein Separations

The resolving power of displacement chromatography using low-molecular-weight displacers was investigated using a model mixture containing bovine and horse heart cytochrome c. The linear and nonlinear adsorption behavior of these two proteins was examined in cation-exchange chromatography and shown to be quite similar. Furthermore, an analysis of the dynamic affinity of these proteins indicated extremely similar affinities under displacement conditions. Despite the extreme similarities in the adsorption behavior, displacement chromatography using a protected amino acid displacer resulted in excellent separation of the proteins with both high yields and purity. These results indicate that displacement chromatography may be efficacious for a wide variety of difficult protein separation problems.

Immobilized metal affinity chromatography: Modeling of nonlinear multicomponent equilibrium

A rigorous multicomponent isotherm for preparative immobilized metal affinity chromatography (IMAC) must consider the multipointed nature of adsorption, the possibility of steric hindrance of the stationary phase upon binding of macromolecules, and the role of the mobile-phase modifier. In this paper, the metal affinity interaction chromatography (MAIC) model, a formalism which addresses all three of these issues, is presented. The linear and nonlinear adsorption behavior of proteins as a function of mobile-phase imidazole content is considered. Numerical simulations of nonlinear chromatography, employing MAIC equilibrium, are seen to accurately predict the experimental results in various modes of nonlinear IMAC chromatography. In frontal chromatography, the model is seen to accurately describe the adsorption phenomena, including induced imidazole gradients. In step gradient and displacement chromatography, the results presented in this manuscript demonstrate the ability of the MAIC model to predict multicomponent equilibrium in IMAC systems and establish this model as a powerful tool for studying the operation of IMAC separations.

Diffusion in Saturated Soil. II: Results for Compacted Clay

The effective diffusion coefficients, D*, of three anions (Br-,Cl-, and I-) three cations Cd2+,K+, and Zn2+ diffusing in two compacted clay soils, kaolinite and Lufkin clay, are measured. The ions are contained in a simulated waste leachate. The effects of molding water content and method of compaction on the measured D* values are evaluated for kaolinite. The calculated D* values varied between 4×10-10m2/s and 2×10-9m2/s and, based on the results for chloride diffusion in kaolinite, are relatively insensitive to molding water content and compaction method. The measured D* values for Cl- and Br- in kaolinite are in excellent agreement with previous studies, but the D* values for the cations are relatively high. High D* values for the cations are attributed to nonlinear adsorption behavior at relatively high concentrations and to the possibility of chemical precipitation of the heavy metal species (Cd2+ and Zn2+). Also, D* values determined from reservoir concentrations typically are higher than D* values determined from soil concentration profiles.

Diffusion of inorganic chemical species in compacted clay soil

This research was conducted to study the diffusion of inorganic chemicals in compacted clay soil for the design of waste containment barriers. The effective diffusion coefficients ( D ∗ ) of anionic (Cl −, Br −, and I −) and cationic (K +, Cd 2+, and Zn 2+) species in a synthetic leachate were measured. Two clay soils were used in the study. The soils were compacted and pre-soaked to minimize mass transport due to suction in the soil. The results of the diffusion tests were analyzed using two analytical solutions to Fick's second law and a commercially available semi-analytical solution, POLLUTE 3.3. Mass balance calculations were performed to indicate possible sinks/sources in the diffusion system. Errors in mass balance were attributed to problems with the chemical analysis (I −), the inefficiency of the extraction procedure (K +), precipitation (Cd 2+ and Zn 2+), and chemical complexation (Cl − and Br −). The D ∗ values for Cl − reported in this study are in excellent agreement with previous findings for other types of soil. The D ∗ values for the metals (K +, Cd 2+, and Zn 2+) are thought to be high (conservative) due to: (1) Ca 2+ saturation of the exchange complex of the clays; (2) precipitation of Cd 2+ and Zn 2+; and (3) nonlinear adsorption behavior. In general, high D ∗ values and conservative designs of waste containment barriers will result if the procedures described in this study are used to determine D ∗ and the adsorption behavior of the solutes is similar to that described in this study.